The setup is similar to quantum eraser experiments (see below). The laser pulses at regular intervals to send bunches of photons. They get split in half as entangled particles. One beam is sent 1 light year in one direction to (Z) and the other sent 1 light year in the other direction to the set of detectors (A,B,C,D). If the mirrors (X & Y) are in place at the detectors and they cause A & B to measure which slit the photons pass through then they will collapse the corresponding entangled particles at Z. An observer at Z will not see an interference pattern for that bunch of photons. However if the mirrors (X & Y) are removed then the observer at Z will see the entangled bunch of photons form an interference pattern. It seems like you could then use whether each incoming bunch of photons forms an interference pattern or not as binary. Obviously this setup doesn't work because FTL communication is impossible, I'm trying to understand why it wouldn't work.
Note in response to the first answer: Sending entangled light particles a light year to a detector is of course difficult or impossible. I chose an arbitrarily long length to exaggerate its effect. The same question could be posed with a light beam of any length.